9127
J. Phys. Chem. 1992,96,9127-9132 (1 3) Girard, P.; Couffignal, R.; Kogan, H. B. Terruhedron Lerr. 1981,22, 3959. (14) Wolfe, S.;Pilgrim, W. R.; Garrard, T. F.; Chamberlain,P. Can. J. Chem. 1971,49, 1099. (15) Baranovic, G.; Colombo, L.; Furic, K.; Durig, J. R.; Sullivan, F.; Mink, J. J . Mol. Srrucr. 1986, 144, 53. (16) Hoshi, T.; Okubo, J.; Kobayashi, M.; Tanizaki J . Am. Chem. SOC. 1986, 108, 3867. (17) Dale, W. J.; Starr, L.; Sterobel, C. W. J. Org. Chem. 1961, 2225. (18) Hashimoto, S.;Shimojima, A.; Yuzawa, T.; Hiura, H.; Abe, J.; Takahashi, H. J . Mol. Srruct. 1991, 242, 1. (19) Kunimatsu, N.; Takahashi, H. To be published. (20) Colombo, L.; Kirin, D.; Volovsek, V.; Lindsay, N. E.; Sullivan, J. F.;
Durig, J. R. J . Phys. Chem. 1989, 93, 6290. (21) Locoge, N.; Buntinx, G.; Ratovelomanana,N.; Poizat, 0. J. Phys. Chem. 1992,96, 1106. (22) Scaiano, J. C. J . Phys. Chem. 1981,85, 2851. (23) Hayon, E.; Ihata, T.; Lichtin, N. N.; Simic, M.J. Phys. Chem. 1972, 76, 2072. (24) Juchnovski, I. N.; Kolev, T. M. Specrrosc. Lerr. 1986, 10, 529. (25) Shida, T.; Iwata, S.; Imamura, M. J . Phys. Chem. 1974, 78, 741. (26) Ichikawa, T.; Ishikawa, Y.; Yashida, H. J . Phys. Chem. 1988,92,508. (27) Kamlet, M. J.; Abboud, J. L. M.; Abraham, M.H.; Taft, W. J. Org. Chem. 1983,48, 2877. (28) Wilson, E. B., Jr. Phys. Rev. 1934, 45, 706.
Low-Frequency Raman Spectra from Concentrated Aqueous Hydrochloric Acid. NormaCCoordlnate Analysis Using a “Four-Atomic” Model of C, Symmetry, (H20)2(HBO+)(cl-H20) G.E.Walrafen’ and Y.C . Cbu Chemistry Department, Howard University, Washington, D.C. 20059 (Received: April 3, 1992; In Final Form: July 16, 1992) Low-frequency,X ( Z 2 )Y,X(ZX)Y,and isotropic, BoseEinstein corrected, Raman spectra were obtained from concentrated aqueous HCl. Normal-coordinate analysis of the intermolecular vibrational frequencies was carried-out with a “four-atomic” (H20)2(H30+)(CI-Hz0) model of C, symmetry using structural parameters obtained from X-ray RDF data. The C1- ion is directly hydrogen-bonded to one of the protons of H30+ in this structure, i.e., one C1- is interspersed between, and hydrogen-bonded to both, a proton of H30+and an outer H20. The C, structure fits the Raman data when [H20 [HCI] < 4, whereas H904+fails to explain a key isotropic feature. The C, model also explains both of the 3.13- and 3.63- X-ray RDF peaks’ as the two 0 4 1 distances of the C, structure. These two 0-C1 distances and the 0-0 RDF distance of 2.52 A place the C1- above the three protons, Le., the line from the 0 of H30+to C1- differs only =9O from the 3-foid axis of H30+. This C, model is analogous to that used by Gigu5re2to explain the weakness of HF, but the hydrogen bonding between C1- and H30+is much weaker than that between F and H30+,in accord with the greater acid strength of HCl.
u
Introduction In this work we present evidence for a structural model of concentrated aqueous HC1 solutions which involves interspersing, into H904+,one Cl- ion, between a proton of the H30+core, and one of the outer H 2 0 molecules. See Figure 1. This model refers to high HCl concentrations at which the stoichiometric [H20]/[HCl] ratio is near, and below, 4. At very much lower HCI concentrations it is possible that the C1- ion, surrounded by several (four to six) H 2 0 molecules of hydration, plus H904+, and/or its higher hydrates, H904+(H20),, may be significant. An X-ray RDF for [H20]/[HCI] = 3.99 was reported previously by Triolo and Narten.’ This definitive RDF showed a completely resolved 0-0 peak near 2.52 A, which means that some hydrogen bonds (between the H30+core and surrounding H 2 0 molecules) are almost symmetric. (The proton is exactly centered between two 0 atoms, -2.4 A apart, in a symmetric hydrogen bond?) However, a further intense, completely resolved, feature near 3.13 A was only explained in general terms,I and the explanation offered for the resolved 3.63-A peak as a CI-CI distance’ now seems improbable; see the recent review of Ratcliffe and Irish4 We have obtained and analyzed low-frequency, intermolecular Raman data from concentrated HCI solutions (polarized, depolarized and isotropic, all Bose-Einstein (BE) corrected). We previously attempted an analysis of these data based upon normal-coordinate analysis of Hg04+, but this model did not predict a key isotropic Raman feature observed near 125 cm-’.’ The 125-cm-’ feature was assigned to first-shell hydration of the C1ion,’ an unsatisfactory procedure because H30+and C1- almost certainly share H 2 0 molecules at very high HCl concentrations, [H20]/[HCl] 5 4 . We now present a normal-coordinate analysis of Raman data using a “four-atomic” C, structure, with an interspersed C1- ion, as described above. The structural parameters for this model were 0022-365419212096-9127S03.00IO I
,
obtained from X-ray’ and other data.“ However, the 3.13-A RDF peak was reinterpreted by us as the closest of the two 0 4 2 1 distances of our C, structure (Figure l), a reinterpretation considered reasonable by Narten.6 The 3.63-A peak then follows naturally as the second closest O-CI distance of our C structure (Figure 1). This assignment of the 3.13- and 3.63-6 peaks as the closest and second-closest 0421 distances, in conjunction with the 2.52-A 0-0 distances of the two nearly symmetric hydrogen bonds, (Figure l ) , means that the O-Cl- line is 9.3O from the 3-fold rotation axis of H30+,a condition that is reasonable from Coulomb’s law, because the positive charge is associated with the protons. Moreover,our assignment of the 2.52-, 3-13., and 3.63-A peaks demands that the Dsecond-0 distance be 4.2 A in exact agreement with a fourth resolved peak in the RDF at 4.20 A.’ Our RDF distance assignment also yields a value of 112.9O for the 0 0angle of our C, structure. (Detailed angles and distances calculated from our model are given below and in the caption of Figure 1.) We find that the “four-atomic” C, model with interspersed C1fits the Raman data very closely and explains the 125-cm-l isotropic feature, naturally, as the O-CI stretching, normal mode of the C, structure, in contrast to our previous approach in which the 0421 stretching was an appendage, i.e., assigned to fmt-shell hydration of the chloride ion. Moreover, the mass density of the HCI solution, calculated from this model, is in good agreement with experiment, whereas the mass density calculated from the H904+ plus C1--H20 does not agree with the density for [HzO]/[HCl] 5. We used the GF matrix elements derived by Cotton and Horrocks’ in our C, normal-coordinate analysis, but we modified the calculation procedure by determining the eigenvalues of the asymmetric 6 X 6 matrix.8 This 6 X 6 matrix reduces to a 4 X 4 matrix for the polarized or isotropic A’ modes and to a 2 X 2 matrix for the A” modes, which are depolarized and missing in 0 1992 American Chemical Society
9128 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
Walrafen and Chu
2 4 sm
110
10
/ '
300
37 m
-1
R.10
107.10
141 OI
imm
Y1l.10
cm"
Figwe 2. BostEinstein corrected isotropic (see text) Raman spectrum from 36.9 wt 8 aqueous HCI. Spectra were obtained with an Instruments S.A. U- lo00 holographic-grating double monochromator. Slit widths corresponding to 5 cm-I were used. 488.0-nm argon ion laser radiation at a power level of 200 mW was employed for excitation. Two-Gaussian deconvolution of the isotropic Raman spectrum was accomplished with a du Pont 3 10 curve resolver, an analog computer. Sct the Gaussian components whost central frequencies are shown above half-width bars, 128 and 206 cm-'.Part of a third Gaussian component is shown to the right in the figure. This resulted from deconvolution of a remaining part of the spectrum (not shown) from which the heavy, horizontal baseline was determined.
- exp(-hcB/kTJ,
"
0
7 1
Figure 1. "Four-atomic" C, model. (a) Nuclear positions, open circles. 1, 2,3, oxygen nuclei. 4, chlorine nucleus. 5.6.7, protons. The C, plane
contains 2,5, and 4 and bisects the 1-2-3 angle, 8. The value of 8 used for the figure is exactly 113'. The angle a is defined by 4-2-3 (or 4-2-1). a = arccos (a2+ b2 c2)/2ub, where u = 2.52 A = 1-2 or 2-3, b = 3.13 A = 2-4, and c = 3.63 A = 1 4 or 3-4. a = 79.15O. H30+ core, 5,6,7,2. Short rods refer to hydrogen bonds. 2-3 and 2-1.2.52 A, i.e., these hydrogen bonds are nearly symmetric and assumed to be linear. Key distance 5 4 , calculated, 2.86 A, see text. Distance 1-3, calculated, 4.20 A, agrees with peak in X-ray RDF, scc text. Distance 2 to center of 1-3 line, 1.39 A, distance 4 to center of 1-3 line, 2.96 A, angle 4-2-5.65.01 O , angle 4-5-2.97.1 1 O, angle 2 4 5 , 17.87'. angle 4-2 to center of 1-3 line, 70.0S0, key angle 8, 180' minus angle 5-2-to center of 1-3 line, 8 = 44.934O, all calculated, see text. The 2-4 line lies ==9O off of the 6-5-7,3-fold rotation axis which passes through 2, slightly to the right in the figure; this places the chloride ion almost directly above the oxygen atom, 2, and above the three protons, a favorable position, electrostatically. Protons attached to 0 atoms, 1,4, not shown. (b) Same as (a), but shaded atoms now shown to size. 4-8-9 refers to the (CI-H20)m a s int of the yfour-atomic"model. Angle 5-4-9, -160'. 4-8, about 2.86 CkH distance, 8-9, about 0.97 A. Both parts (a) and (b) refer to the same perspective view, looking down, and from the side.
-
the isotropic Raman spectrum. We calculated the eigenvalues using the HQR algorithm for real Hessenberg matrices.* Cotton and Horrocks' provided complete details of the displacement coordinates and F and C matrix elements. Nevertheless, we repeat them here in the appendix, for the convenience of interested readers. We obtained the required frequency values from Gaussian deconvolution of the polarized, depolarized, and isotropic Raman spectra. The results are now described.
Raman Data An isotropic Raman spectrum corracted for the one-phonon BoseEinstein (BE) factor, that is, (I[X(ZZ)yl- 4/$[X(Zx)lq1[ 1
is shown in Figure 2. The use of the BE factor is absolutely necessary for the correction of low-frequency Raman spectra; see Placzek9and McQuarrie.Io It is incorrect not to use it; low-frequency Raman spectra without BE correction do not relate to the phonon density of states. The isotropic Raman intensity, as formulated above, is a rigorous consequence of quantum mechanics.I0 Moreover, the isotropic speztrum provides a direct method for the relative enhancement of the contributions of the most polarized modes, such as the symmetric stretching vibrations, compared to the less polarized and completely depolarized modes, deformation vibrations and asymmetric stretching, respectively. This enhancement dues not depend upon computer deconvolution, although such deconvolution is extremely useful as an adjunct. In regard to deconvolution, McQuarrie'O has shown by means of Gram-Charlier series methods that Gaussian peak shapes are correct for dipoldipole molecular interactions. In addition, Chu" has shown that Gaussian Raman line shapes are a direct, rigorous, and necessary consequence of dispersion-bundle theory, derived from the Klein-Gordon equation, in which the velocity is the phonon velocity. See also ref 12. Figure 2 indicates an asymmetric isotropic Raman contour which peaks near -200 an-'.The comsponding isotropic Raman spectrum from pure water shows virtually zero intensity over the same range of Raman shift^,^ and this zero intensity from pure water is a critical test of the accuracy of the isotropic Raman spectrum from concentrated HCI, as well as of the corresponding depolarization ratios, obtained under the same experimental conditions. If the high-frequency isotropic spectrum, Figure 2, is folded back onto the low-frequency part, using 206 an-'as the fold, it is obvious that a second, broad component is present. Also, the intensity difference obtained from this procedure indicates that this second component peaks in the general vicinity of -130 an-'. This conclusion is not dependent upon any assumed or specific component function, except that the components must be symmetric. The sdcond isotropic component obtained by the above empirical method is just the broad component which could not be explained by previous normal-coordinate analysis.' No normal-mode frequency of H904+ even approaches 130 an-'. Hence, it is not necessary to use Gaussian deconvolution to determine that the isotropic spectrum is incompatible with the H904+ structure. Nevertheless, Gaussian computer dmnvolution is an important refinement.
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9129
Low-Frequency Raman Spectra from HCl(aq) TABLE I"
X(ZZ)Y
X(ZX)Y
X(ZZ)Y 32.1 wt % HCI
43 cm-l 99 167
49 105 168
52 113 172
53 108 169
X(ZX)Y
-
216 (17)
(15)
TABLE I' d, = 3.13 A d2 = 2.52 A a = 79.15' Mo 17.01 Mc,= 53.47 M H ~= O 18.02
K 1 = 10 500 dyn/cm (MIstretch) K2 = 19000 (0-0 stretch) K,/d,d, = 2000 Kaaldld2 1000 Kk/d2 = 10 KWld2 6 2Kd/dld2 = 10 q/(d2)2 = 3000
34.6 wt % HCI
-
215 (14)
(19)
36.9 wt % HCI (isotropic) 128
206
'Values in cm-I. Values in parentheses refer to components which are mt normal modes of the "four-atomic" treatment but which were obtained from Gaussian deconvolution. Dashes in the X(ZX)Y column refer to components seen in the X(ZZ)Y spectrum, but missing in the X(ZX)Yspectrum. The spectrum of Figure 2 was deconvoluted with Gaussian components. This procedure revealed two major Gaussian components, shown near 128 and 206 cm-'in the figure. (Nofurther componentsare warranted by the signal-to-noise ratios of the data, and by the accuracy of the deconvolution method.) Figure 2 refers to 36.9 wt 3'% HCI for which [H20]/[HCl] = 3.46. However, the corresponding isotropic Raman spectra and Gaussian component parameters for 34.6 and 32.1 wt % HCl are not different within the experimental errors of the data and the deconvolution procedure. The BE corrected X(ZZ)Y and X(ZX)Y Raman spectra from 36.9,34.6,and 32.1 wt % HCl are not shown here. The X(ZZ)Y spectra all show intensity maxima near 50 and 165-170 cm-I. The X(ZX)Yspcctra all show a peak near 43 cm-'with a pronounced shoulder near 155 cm-I. Gaussian component parameters obtained by deconvolution of the X(ZZ)Y and X(ZX)Y Raman spectra are not significantly different in the 32.1-36.9 wt 96 range. Deconvolution of the X(ZZ)Y spectra with four Gaussian components, and of the X(ZX)Yspectra with three Gaussians was conducted. An extra Gaussian at extremely low frequencies was required in each case, which makes the total numbers actually five and four, but this extra Gaussian component is not a normal mode of the "four-atomic- approximation. The extra very lowfrequency Gaussian component is discussed below and treated by a separate analysis. Values for this extra mode occur in parentheses in Table I. See discussion of this mode near end of article. The fact that the 2 l h - I component is missing in the X(zX)Y spectrum, Table I, means that this component is very highly polarized. The isotropic spectrum indicates two Gaussian components at 128 and 206 an-'.This observation indicates that the 128-cm-'component is also highly polarized. Both modes are thus almost certain to arise from totally symmetric stretching vibrations of the intermolecular structure. Completely depolarized modes (depolarization ratio = 3/4) must be absent, entirely, from the isotropic spectrum. Conversely, completely polarized modes (depolarization ratio = 0) are absent from the X(ZX)Y spectrum. The X(Z2)Y spectrum is a combination of modes of varying degrees of depolarization. Consider two single oscillators, A and B, having equal X(ZZ)Y intensity at the same exact Raman frequency shift, a. Assume that the depolarization ratio of A is 0.02and that the depolarization ratio of B is 0.65,which means that the radiation is still polarized, albeit weakly. The A/B intensity ratio in the isotropic spectrum will be 7.3,but the A/B intensity ratio in the X(Zz)Y spectrum is 1. Such relative intensity enhancement is involved in the results presented in Table I. This explains why only two components can be deconvolved in the isotropic spectrum, compared to 3 or 4 in X(ZX)YandX(ZZ)Y. Of course, strong overlapping of the broad components is also involved in the results of the table. Moreover, there is some experimental error, both in the spectra and in their deconvolution, which means that the isotropic value of 206 cm-I,
@ = 113'
A' modes, polarized v, = 210 cm-l ~2 = 136 v j = 95 V o = 57
Results
A" modes, depolarized V) = 188 ~g = 42
'Morefers to H30+minus 2 protons, and Mcl refers to CI--H20. TABLE III
obsd, Gaussian component freq," cm-l
calcd "four-atomic" C,freq, cm-]
43 53 99-113 128 167-172 206
42 57 95 136 188 210
obsd, Gaussian component freu. cm-'
calcd C,,, frep
14-19
17-22
a The experimental uncertainties in the component frequency values are about 1 5 cm-l near 206 cm-', and they increase somewhat near 43 cm-I.
and the X(ZZ) Y values of 21 5-216 c m - I refer to the same mode.
Normal-CoordinateAnalysis Pad Interpretation Structural parameters and values for the three different masses used h o n e representative example of our "four-atomic" C, normal-coordinate analysis are listed in Table 11. See also Figure 1. Table I1 also lists values of the nine force constants which yielded the six normal-mode frequencies presented in the table. These calculated normal-mode frequencies are compared with the experimental Gaussian component frequencies in Table 111. The X-ray RDF distances of 3.13 and 3.63 A, Figure 1 ,define the angle a,4-2-3 or 4-2-1, when these distances are interpreted as the first and second closest 0 4 1 distances of our C, structure. a = a r m s (a2 b2 - c2)/2ab. a = 2.52 A, b = 3.13 A, and c = 3.63 A. a = 79.15O. 9, = 113O, which is the same as the H-O-H angle of the H30+core. (,9 = a r w s ([(4.20)2- 2(2.52)2]/[-2(2.52)2]).)From a, b, and c and from the 0-H distance, 7-5, Figure 1, 0.97 A, it is possible to calculate the 0-H-Cl angle, 2-5-4, and the H-Cl distance, 5-4. The calculated H-Cl distance is 2.858 A, and the 0-H-Cl angle is 97.113O. (Use the numbering, HIH2H30+,and define the HIOH2plane as the base plane. A second plane perpendicular to the base plane, bisects the HIOH2angle, and passes through 0 as well as through Hp The bisector line in this plane can be shown to forms an angle 6 of 44.9335' to the 0-H3line, when the three H-0-H angles are all exactly 113O. This follows from two identities involving the dot product of the unit vectors, e, = 2-1, and e3 = 2-5, Figure 1, whence B = a r m s ~[cos(l13)[/[-cos(56.5)]). The bisector of the 0-04angle, 3-2-1, Figure 1, which lies in the 0-0-0 plane, forms an angle of 70.053O with the 2-4 line, Figure 1. The angle 4-2-5 is thus 65.014O. 2-4 and 2-5 are known distances, from which 5-4 is calculated to be 2.858 A, using 4-2-5 as 65.014O. When 2-4,2-5,and 4-5 are known, an angle of 97.113O results for 2-54.) We have also calculated the angle between the 3-fold rotation and the 0 4 1 line. This angle, 6, is 9.3O. The fact axis of H30+
+
Walrafen and Chu
9130 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
that 8 is not zero, however, is definitely not the basis for the present C, symmetry (it merely agrees with this symmetry). The main reasons for C, symmetry involve the two nearly symmetric hydrogen bonds whose 0-0 distances are 2.52 A and the fact that O-H-Cl forms a plane which bisects the O-0-0 angle and is perpendicular to the O-0-0 plane. The four symmetric A’ vibrations are polarized in the Raman spectrum. The two remaining A’’ vibrations are depolarized and absent from the isotropic Raman spectrum. vlA’ refers to symmetric stretching of the two H 2 0mass points against the 0 of the H30+core,whereas v f l is the cortesponding asymmetric stretching. vzA’ refers to stretching of the (CI--H20) mass point against the 0 of the H30+core. v3A’ refers to symmetric o-00 bending, that is, the two H 2 0 mass points move such that the O-0-0 angle, 8, changes (Figure 1). The other symmetric deformation is the in-plane bending, v&. The O - o c l angle is 01 (Figure 1). Change of a yields v6A”, the asymmetric, out-of-plane deformation. The 2.52-A 0-0 distance is almost as small as that of known symmetric hydrogen bonds, 2.4 A.3 Accordingly, quantum mechanical proton tunneling is expected to occur in the two 0-H-0 bonds (Figure 1). We ignored the two corresponding protons in our mass assignment because they are partly near the H30+core and partly near the two H20mass points, when tunneling occurs. This procedure resulted in the best experimental agreement. However, we did not ignore the third proton of H30+-weincluded it with the 0 mass of the H30+core. This again yielded the best experimental agreement. It should be emphasized that we tried a very large number (many tens) of combinations of structural parameters, masses, and force constants. Values listed in Table I1 were obtained from one of the more successful trials, but many other trials were essentially as good. Moreover, one set of calculated values, not given here, provides extremely close agreement with the experimental data. But we do not give these values here, because the experimental data are uncertain to some f5 cm-*,and thus exact agreement is not significant and not necessary. The important point is that the various force constants change very little once a family of fits has been obtained that is close to the Raman data. It should also be emphasized that the fitting proccdure is in a sense self-constraining. For example, if one changes a given force constant in the hope of providing better agreement with one specific mode frequency, one often finds that the agreement with two other mode frequencies is adversely affected,e.g., large positive error in one and large negative error in the other. Moreover, some pairs of force constant choices produce negative mode frequencies, which is impossible. We also placed additional “chemical”constraints on the mode frequencies, in addition to the foregoing constraints of the calculation. These constraints on the frequencies are as follows:
> v3, v4, v6 stretching > deformation V I , v2,
vI
v.5
(1)
= v s (approximate)
(2)
> v2
(3)
> v2 v 3 > v4 v3 >
(4)
v1 Us
(5)
(6)
(approximate) (7) After we had thoroughly tested the program to determine that it was correct and reliable, we were able to converge to good agreement with experiment in about 2-3 weeks of force constant iteration and calculation, using the foregoing “chemical constraints”, plus the built-in self-constraints of the program. 01 is f i x 4 at 79.1S0, of course, when the 3.13- and 3.63-A distances are used. B is also fixed at 112.9O by the 2.52- and 4.20-A 0-0 distances. Nevertheless, we tried the following variations: a from 78 to 79O, B from 112 to 114O, K22from 10oO v4 a v6
to 4000, Ko/dld2from 2000 to 3000, Kuu/dld2= 1O00, Kk/d2 = 10, KWJd2= 6, Kd/dld2 from 0 to 10, and K,/d$ from 2800 to 3000 (all force constants in dyn/cm). We also tned Mo from 16 to 19, and Mc,from 35.5 to 54.5 (M= molecular weight; 0 refers to H30+ and C1 to (C1--H20)). We also tested our computation procedure against vibrational frequencies reported for F$O, Cl$O, and Br$07J3 and obtained excellent agreement. The density of 33.598 wt %I HCl ([H20]/[HCl] = 4) is 1.17 g/cm3 at 25 OC. We estimate that a structural model which explicitly includes the Cl--HOH structure of the (CI--H,O) mass point, plus other H 2 0 protons, 1, 3, Figure 1, has an effective volume (including void spaces) of 145-150 A3, namely, a 9 A (length) times -16 A2 (area). This volume contains four H 2 0 masses and one HCl mass (stoichiometrically),i.e., the total mass is 108.52/NA grams. The density is thus roughly 1.2 g/cm3. A model involving H904++ C1- H 2 0 is much bulkier than our C, model. We take account, of course, of the extra H 2 0 molecule in the total mass. In this second model we considered three symmetric h rogen bonds to the H30+core all having 0.0 distances of 2.52 with a chloride ion at a 0 4 1 distance of 3.13 A to the central 0 of the hydronium cation (the chloride approaches the side opposite the lone pair electrons of the central 0 atom, i.e., nearest to the three protons, or the concave side of H30+). The 0 of the extra H 2 0 molecule is then placed 3.13 A from the chloride ion (concave side). In this case the mass is 126.5/NA,and the volume is a 9 A (length) times =32 A (area), including void spaces. V = 290 A’. The density that results is a0.7 g/cm3, which is greatly in error, because the experimental density Is 1.14 g/cm3 for 28.82 wt %I = 5 H20/HCI. Hence, the C, model seems preferred on the basis of the above density comparisons. We have also considered three-dimensional structures made up by repetition, both sideto-side and end-to-end, of our C, model. This is extremely revealing and impacts directly, and very importantly, on the question of whether or not our C,, model A, is preferable to H904+ CI-(H20), model B. We find that three-dimensional hydrogen-bonded structures of our model A contain model B within them. Hence, it is extremely important to realize that one difference between model A and model B is a matter of counting in a three-dimensional hydrogen-bonded network. When this is understood, the problem with model B becomes clear. Model B docs not appear to be the basic unit of the repetition, as o p p e d to model A. Moreover, if one tries to collstruct a network purely from model B, one finds that repetition becomes extremely difficult and does not make good sense in terms of hydrogen bonding. It should be made clear here, however, that we definitely do not advocate a lattice model. On the contrary, the liquid must have much randomnets in it. We feel, nevertheless, that a successful model should lend itself to dense packing within the context of a network having hydrogen bonds whose angles and 0-0 distances are not abnormally strained and long. It should also be emphasized that the distances used in the present C, model correspond to maxim, i.e., peaks in the RDF.’ The X-ray peak distance values were used, of necessity, in our nonnal-coordinate analysis, because they are unique features of the RDF. However, the RDF peaks are broad, which means that a distribution of distances is involved, which, in turn, requires a distribution of angles. The stretching and deformation force constants must also be distributed because of these distance and angle distributions. This leads to the large breadth observed in the Raman spectra, and the corresponding Gaussian components. It implies, moreover, that there must be a distribution of C, models, not just the single model used here. This distribution of models provides another great source of randomness to the liquid structure, in addition to the randomness of the way in which the C, structures are oriented with respect to each other. We also used Gaussian components centered at the six normal coodinate frequencies, Table 11, to synthesize the X(2Z)YRaman spectrum (1 5-20-cm-l region excepted). This provided only slightly better fits than the previous Gaussian analysis, and it greatly overdetermined the simulation (lacked uniqueness).
+
2
+
Low-Frequency Raman Spectra from HCl(aq) Even our experimental Gaussian analysis, however, always required an extra component (see values in parentheses in Table 11) near 15-20 cm-l. A frequency this low is nor predicted by the present normal-coordinate analysis, but this low frequency may refer to a mode ignored by our "four-atomic" approximation, and/or it could result from the effect of the BE function on the stray light very close to the exciting line. We conducted an additional analysis, beyond the "four-atomic" normalcoordinate analysis,to determine if the extra low-frequency mode observed near 15-20 cm-l could reasonably be explained as a deformation vibration, as opposed to an artifact of the BE correction. H.*-CI--*H bending is precluded by our four-atomic approximation because (C1--H20) is treated as one mass point. This type of bending motion should lead to a very low vibrational frequency. Accordingly, we used an additional (very simple) normal-mode calculation to treat the situation which arises when the motions of the chloride ion are separated from the motions of the water molecule to which it is hydrogen bonded. We approximated the H--Cl-*-H deformation as the bending of a C, XY2molecule.14 We used mx = 18 (H20) and my = 35.45 (Cl). We mered values of the X-Y-X angle, a,from 160 to 165' in l o increments. Fortunately, the force constant, K1, for H-(CI-H20) stretching, needed for this new calculation, had been obtained previously in our "four-atomic" analysis (see Table 11) 10500 dyn/cm. The stretching frequency needed is 128 an-', the experimental value, see Figure 2. 128 cm-' is u2 in the "four-atomic" model, but it now becomes uI in the C, model. We varied a from 160 to 165', and we varied K2,the C, bending force constant, from lo00 to 500 dyn/an. A K2 of 600 dyn/cm yielded a u2 value of 17.1 cm-l, for a = 163'. When we used K2 = lo00 dyn/cm, we observed that u2 moved up to 21.6 cm-l. This latter rcsult may be more realistic than the former, because K2 is often roughly one-tenth of K l , viz., 1000 versus 10 500 dyn/cm. The above approximate calculations are sufficient to suggest that a Gaussian component whose frequency occurs between 15 and 20 cm-l may be a real mode of the vibrational Raman spectrum of concentrated aqueous hydrochloric acid solutions, in addition to the other normal modes resulting from the "fouratomic" approximation used in this work. Finally, it should be noted that the present C, model is the HCI analog of the model used successfully by GiguZre2to explain the unexpectedly weak acidity of HF. Because the O-H-421- hydrogen bond is weaker than the 0-H-F hydrogen bond, it follows from the GiguZre model that HCl should be a stronger acid than HF, as observed. Moreover, it is not inconceivable that structures similar to that described here for HCI may also be important for very concentrated aqueous HBr and HI. A model very similar to the present C, model has also been used to explain the hydration and desorption kinetics of a wetted BeF2 glass surface; see especially Figure 6 of ref 15.
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9131 A" species
R5 = ( 4 d 2 - Ad3)/.\/z R6 = (Aal - A a 2 ) / f i dl = C1-0 distance: d2 and d3,O-H20 distances, al is the angle between dl and d2;a2 is the angle between dl and d3;8 is the H20--0--H20 angle. F Matrix Elements: FI1 = K1 F12
= l/ZKIu F14 = KIP
Fl3
F33
= fiKuL3 F M = KO
F34
= K2 - K22 F56 = K2u - K2d F66 = K, - K,,) K I is the (21-0 stretching force constant K2 is the 0--H20 stretching force constant K, is the force constant for bending of a Ks is the force constant for bending of 8 F55
K,, is the interaction force constant, between aIand a2 KUs is the interaction force constant, between a and 8 K12is the interaction force constant, between d l and d2 K I a ,K2., and K2,! are interaction force constants between dl and d2 with the adjacent angle, al,or opposite angle, a2 K I Pand K2, are interaction force constants between dl or d2 with the angle fi K2, is the interaction force constant between the two bonds, d2 with d3 C Matrix Elements: GI1 = Po + PCI
GI2 = f i ~ o cos a
cI3= - f i k p 2
sin a GI4= -2p2pO cos a tan 8/2
G23
G33 =
R3 =
PO
= -T-(272 sin a! ~ 2= 4
Symmetry Coordinates:
R2
dl + COS 8) + PHIO
G22
c, symmetry
Ad1
(Ad2 + Ad3)/l/Z
+ Aff2)/l/Z R4 = 46
fiK28 = Ka + Kuu
F24
Appendix. Symmetry Coordinates and C and F Matrices for
RI
= K2 + K22 K2a + K2aI
F22
F23
Acknowledgment. Private conversations with D. E. Irish (several), A. H. Narten, and F. H. Stillinger are gratefully acknowledged. This work was supported in part by NASA and was conducted under the CSTEA program at Howard University, NAG W2950.
A' species
= fiK12
PO
~ [ 4 7 1 COS ~ 2 a
COS
ff
+ 71(1 + COS @)I
-fipop2 sin 0
+ 7l2(W8 + 1) + 2 ~ 2 ~+1
9132
J . Phys. Chem. 1992,96,9132-9139
= l/dl P2 = l/d2 = P I - p2 COS CY = p2 - PI COS a PI
71
T2
Po
= 1/Mo
= l/MCl 1/MHzO Mo is the mass of H30+ minus 2 protons Mcl is the mass of C1- H 2 0 MHl0 is the mass of the H20 molecule PCl
PHzO
+
References and Notes (1) Triolo, R.; Narten, A. H. J . Chem. Phys. 1975, 63, 3624. (2) Gigu€re, P. A. J . Chem. Educ. 1979, 56, 571. (3) Walrafen, G. E.; Chu, Y. C. In Proton Transfer in Hydrogen-Bonded Systems; Bountis, T., Ed.; Plenum: New York, 1992.
(4) Ratcliffe, C. I.; Irish, D. E. In Water Science Reviews; Franks, F., Ed.; Cambridge University Press: Cambridge, 1988. (5) Hams, D. C. Quantitative Chemical Analysis; Freeman: New York, 1982; p 158. (6) Narten, A. H., private conversation, 1992. (7) Cotton, F. A,; Horroch, W. D., Jr. Spectrochim. Acta 1960,16,358. (8) The present C, model involves a 6 X 6 CF matrix. This matrix may be. reduced to a 2 X 2 matrix, whose solution is easy, and to a 4 X 4 matrix, whose solution is difficult bccause it is a nonsymmetric matrix. C and F are each symmetric matrices, but GF is generally a nonsymmetricmatrix, unless [C,F]= 0. One cannot use Jacobi's method; see: Maron, M. J. Numerical Analysis; Macmillan: New York, 1982, to obtain the eigenvalues for nonsymmetric matrices. However, we were able to calculate the eigenvaluesfor our 4 X 4 matrix, readily, using the HQR algorithm for real Hessenberg matrices, see: Vetterling, W. T.; Teukolsky, S.A.; Press, W. H.; Flannery, B. P. Numerical Recipes; Cambridge University Press: New York, 1990. (9) Placzek, G. Rayleigh-Streuung und Raman-Effekt. In Handbuch der Radiologie; Marx, E., Ed.; Akademische Verlag: Leipzig, 1934; Vol. VI, 2, pp 205-374. (10) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1976. For the BowEinstein correction to the measured Raman intensity, see. p 472, q s 21-17 and 21-18. For a discussion of the isotropic Raman spcct" and derivationsthereof, see pp 482-489. For G r a d h a r l i e r analysis leading to Gaussian Raman line shapes resulting from dipoltdipole interactions, see p 542. (11) Chu, Y. C. Doctoral dissertation, Physics Department, Howard University, Washington, DC, May, 1991. (12) Walrafen, G. E.; Chu, Y. C.; Hokmabadi, M.S.J . Phys. Chem. 1990, 94, 5658. See eq 1 on p 5660 and discussion thereof. (13) Nakamoto, K. Infrared and Ramon Spectra of Inorganic and Coordination Compounds, 3rd ed.; Wiley-Intersciencc: New York, 1977. (14) Herzbcrg, G. Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold New York, 1945. (15) Walrafen, G. E.; Klein, P. H. J . Chem. Phys. 1987, 86, 6516.
EPR and ENDOR Study of Selected Porphyrin- and Phthalocyanine-Copper Complexes S.P.Creiner,*lt D. L. Rowlands,* and R. W. Kreilick Department of Chemistry, University of Rochester, Rochester, New York 14627 (Received: April 23, 1992; In Final Form: July 30, 1992)
Electron paramagnetic resonance spectra and nitrogen ENDOR powder spectra have been obtained from copper complexes of tetraphenylporphyrin, meso-tetrakis(2-methylpyridinium-N-y1)porphyrin(ortho), meso-tetrakis(4-methylpyridinium-Ny1)porphyrin (para), and phthalocyanine at approximately4 K. All four samples display axial symmetry. The three porphyrins have nearly identical g, and gy values (2.054.2.055) but differ in their g, values (2.186,2.209,2.212). The copper phthalocyanine has axial components equal to 2.060 and a z component of 2.179. CuTPP has the largest axial component of the copper hyperfine tensor, 98.6 MHz compared with values from the other three samples of 80 MHz. The z component of the copper hyperfine tensor is closer in magnitude for CuTPP and copper phthalocyanine (631 and 637 MHz), while for the methylpyridyl species its value is 593 MHz (ortho) and 598 MHz (para). Through analysis of these data, the orientations of molecules contributing to each ENDOR spectrum are readily calculated. The magnitudes of the nitrogen hyperfine and quadrupolar tensors were determined through analysis of the angle-selected ENDOR spectra. The largest component of the nitrogen hyperfine tensor was found to lie along the Cu-N bond axis in each case.
Introduction In an earlier paper, it was demonstrated how angle selection from EPR spectra of randomly oriented samples could be used in the analysis of ENDOR spectra to determine the orientation of the ligand nuclei's hyperfine interaction tensor with respect to the central metal atom's g axis system.' The analysis in that paper was confined to the case in which both the g tensor and metal hyperfine interaction were rhombic with coincident axes. In this paper, we consider angle selection for three copper porphyrins, copper tetraphenylporphyrin, copper meso-tetrakis(4-methylpyridinium-N-y1)porphyrin. copper meso-tetrakis(2-methylpyridinium-N-yl)porphyrin,and also copper phthalocyanine. Each 'Current address: Allied-Signal R&T, 50 East Algonquin Rd. Box 5016,
Des Plaines, IL 60017.
'Current address: Xerox Corp., 800 Phillips Rd, Bldg 205-99P, Webster, NY 14580.
of the molecules has four nitrogen atoms coordinated in a planar configuration to a central copper atom. Each nitrogen atom is magnetically equivalent to its trans neighbor and has coincident hyperfine axes. Nitrogen atoms cis to one another have hyperfine interactions of equal magnitude but with a different orientation and hence are not equivalent. The EPR spectra of polycrystalline or amorphous samples reflect a "powder" average of all molecular orientations with respect to the magnetic field.2-8 If the g and hyperfine tensors are known, one can associate distinct sets of molecular orientations with a given resonant field value. This set of molecular orientations is thereby selected for nuclear resonance by the fucd field setting in an ENDOR experiment. The result is an ENDOR spectrum that reflects the angular dependence of the hyperfine energies of ligand nuclei. Once this angular dependence is known, the geometric location of a ligand proton and spin density at that nucleus can be determined?JO For nitrogen ligands, however, the atom's
0022-3654/92/2096-9132$03.00/00 1992 American Chemical Society
